This invention relates to a method of measuring yield stress in polymer systems. The method was developed and demonstrated using an on-line capillary rheometer. Such a method of measurement has utility in on-line assurance testing of production processes, and could be a suitable replacement for currently used test methods performed off-line.
Rheology is the science of flow and possible elastic deformation of matter. It is concerned with the response of materials to a mechanical force. The flow properties of a simple viscous liquid are defined by its resistance to flow, i.e., viscosity, and may be measured by determining the rate of flow through a capillary.
Such a simple viscous liquid continues to deform as long as it is subjected to a tensile stress or a shear stress. Shear stress is a force applied tangentially to the material. In a liquid, shear stress produces a sliding of one infinitesimal layer over another.
For a liquid under shear, the rate of deformation or shear rate is proportional to the shearing stress. This is true for ideal or Newtonian liquids, i.e. water, but the viscosity of many liquids is not independent of shear rate. Non-Newtonian liquids may be classified according to their viscosity behavior as a function of shear rate. Some liquids exhibit shear thinning, whereas other liquids exhibit shear thickening. Some liquids at rest appear to behave like elastic solids until the shear stress exceeds a certain value called the yield stress (tau.sub.0), after which they flow readily.
Elastic as well as viscous behavior can be observed at the onset or cessation of flow when the applied stress is insufficient to initiate or sustain flow, respectively. The minimum stress required to initiate flow is referred to as yield stress, while the maximum stress observed at the cessation of flow can be referred to as residual stress. Yield stress and residual stress are not necessarily equal. Their values are subject to flow rate and flow history considerations. However, on a reasonable time scale, their values can be considered to be proportional and approximately equal for most materials. For purposes of this invention, specific measurements of residual stress were made, but the results have been reported generically in terms of yield stress.
Shear stress is often plotted against shear rate on plots called flow curves which are used to express the rheological behavior of liquids. Newtonian flow is shown by a straight line, and shear thinning and shear thickening are shown by curves. Yield stress is an intercept or point on the stress (tau) axis of such plots (see FIG. 2 in the drawing, for example). Yield stress, therefore, is a parameter which can be quite useful in characterizing materials. For example, water has a yield stress of zero.
A method for measuring yield stress was discovered while attempting to repeatably calibrate a capillary rheometer. It was discovered that when flow through the capillary was stopped for zero calibration, a residual positive (forward) backpressure proportional to yield stress, remained within the capillary rheometer. By manually reversing the metering pump of the rheometer, a negative (reverse) backpressure was noted. The difference between the positive and negative (forward and reverse) residual pressures is proportional to twice the yield stress, and is independent of the zero calibration value. This discovery was made while using an on-line capillary rheometer for monitoring a silicone sealant mixture.
The mathematical relationship used to make the measurement is defined by the equation: EQU Shear Stress.sub.(Flow) at Capillary Wall=RP/2L
where R is the radius of the capillary, L is the length of the capillary, and P is the pressure drop through the capillary.
Thus, for a given system, the pressure P is a proportional measure of the residual stress.sub.(No Flow) below which flow through the capillary will stop. The most common units for shear stress.sub.(Flow), residual stress, and yield stress.sub.(No Flow), are dynes per square centimeter (dyn/cm.sup.2), Pascals (10 dyn/cm.sup.2 =1 Pa), newtons per square meter (1N/m.sup.2 =1 Pa), and bar (1 bar=1.times.10.sup.5 Pa=14.5 psi).